Question

a string running from the ground to the top of a fence has an angle of elevation of 45°. the string is 12 feet long. what is the distance between the fence and where the string is pegged to the ground? a) 6√3 ft b) 6 ft c) 6√2 ft d) 24 ft e) 2√3 ft f) none of the above.

Explanation:

Step1: Use trigonometry

We have a right - triangle situation where the string is the hypotenuse ($c = 12$ ft) and the angle of elevation $\theta=45^{\circ}$, and we want to find the adjacent side $x$ (distance from the fence to where the string is pegged). We know that $\cos\theta=\frac{x}{c}$.

Step2: Substitute values

Since $\theta = 45^{\circ}$, $\cos45^{\circ}=\frac{\sqrt{2}}{2}$ and $c = 12$ ft. Substituting into the formula $\cos\theta=\frac{x}{c}$, we get $x = c\cos\theta=12\times\frac{\sqrt{2}}{2}=6\sqrt{2}$ ft.

Answer:

c) $6\sqrt{2}$ ft